I think I would just take the combs out of the cast and put them in the queenless hive. If you do it in the evening then most of the foragers in the cast will be at home. You can move many or all of the bars at the same time by putting pieces of wood at right angles to the bars and underneath them, in effect carrying them on rails ( using a top bar for this purpose might do if you have ten or fewer bars ). This means they stay warmer during the move and you're very unlikely to lose or damage the laying queen. I'm assuming the two hives are walking distance apart, and that you have room in queenless hive.

If the colony you're moving them into really is queenless, then everything should go fine.

Some of the foragers from the cast might get confused and try to go home, but they will probably find their way in to the colony in the other end of the hive that currently has two colonies in it, which is fine.

You could use the trick of putting grass into the entrance of the newly created combined colony, forcing all the foragers in that colony to re-orientate, but I'm not sure that's necessary in these circumstances, since losing some of the foragers from the new hive is no disaster anyway.

Just one question: where will we put the cast swarm combs in relation to the combs of the Queenless colony? In the middle? Or at one end?

Not sure !

I would probably keep the cast bars together as far as possible, and put them in roughly the same distance from the hole in the new hive as they are now.

If the queenless colony consists mainly of stores, I might put the stores further away from the entrance than the stores of the cast.

Something like hole -> cast brood -> cast stores -> queenless stores.

But that's only my guess.

Whatever you do, you should keep the cast brood together, with at least one of its own honey bars. That way you know the queen is OK.

Are the two hives completely identical ? If not, you may find that the combs don't fit, in which case you might need to be prepared to do some trimming. That will complicate and slow down the whole operation.

The hives are identical, though the cast swarm has built 5 combs only half the width of the TbH.
The cast swarm are presently using the rear RHS entrance so we could open that hole in the hive we are moving them to??? and put their comb at that end.
The colony already in there is using 3 front holes and one LHS rear hole!

Conserving wild bees

Research suggests that bumble bee boxes have a very low success rate in actually attracting bees into them. We find that if you create an environment where first of all you can attract mice inside, such as a pile of stones, a drystone wall, paving slabs with intentionally made cavities underneath, this will increase the success rate.

Most bumble bee species need a dry space about the size a football, with a narrow entrance tunnel approximately 2cm in diameter and 20 cm long. Most species nest underground along the base of a linear feature such as a hedge or wall. Sites need to be sheltered and out of direct sunlight.